Financial instruments and methods for the housing market

ABSTRACT

A first financial instrument defines an interest in a property, where one or more buyers are given rights on at least part of a selling price of the property. The interest is purchasable by the interest buyers independently of time of sale of the property and independently of change of occupants of the property. A second financial instrument separates habitational rights in a habitable property from non-habitational rights in that property. A combination between the two financial instruments is also provided.

CROSS REFERENCE TO RELATED APPLICATIONS

The present application claims priority to U.S. Provisional Ser. No. 60/893,644 for “Various” filed on Mar. 8, 2007, the disclosure of which is incorporated herein by reference in its entirety.

BACKGROUND

1. Field

The present disclosure relates to the field of financial instruments. In particular, it relates to financial instruments and methods for the housing market. More specifically, it deals with the housing derivatives market and equity financing for housing.

2. Description of Related Art

The commercial real estate market size in the United States size stood at $4.4 trillion by year-end 2000, up 12 percent from 1999. Institutions owned just shy of $2 trillion (or 45 percent) in commercial real estate, while private corporations accounted for the remainder. In 2002, the collective value of U.S. households' home real estate holdings stood at $12.04 trillion, just $3 trillion less than the stock market capitalization of all U.S. firms. The average home is sold every 7 (5 to 8) years. This means the household real estate market size is 1.7 trillion dollars a year. This makes it one of the two largest industries in America. And which high-wheeling professional makes buy and sell decisions in this largest of all markets? Poppas and Mammas across America. Yes, pricing and selling decisions on households are made by the average Joe, with a little advise from realtors, an industry so fragmented and with so little sophistication you can hardly call their advice professional. Furthermore, despite the fact that real estate transactions usually have the largest financial impact of any transactions carried out by most Americans, sales decisions are often made in a weekend, with limited access to the pool of all potential buyers, and without taking advantage of sophisticated and more profitable selling mechanisms such as auctions, etc.

Sellers and buyers of real estate often need the money from the sale of their previous property to buy their new property. This forces them to find a buyer for their old property at the same time as a house available for purchase. This lengthens the time for a successful transaction and reduces the pool of available buyers and properties, resulting in worse matchmaking, which results both in less happy buyers (who need to settle for less desirable homes than they would if they had time to find one without the worry of finding a buyer for their old one) and less happy sellers (who need to settle for lower prices than they would if they had time to find the most interested buyer). Finally, most housing sales decisions are conducted today by amateurs, resulting in suboptimal matchmaking and sales prices.

SUMMARY

According to a first aspect, a financial method is provided, comprising: providing one or more interest buyers with an interest in a property, the interest providing the one or more interest buyers with rights on at least part of a selling price of the property, the interest being purchasable by the interest buyers independently of time of sale of the property and independently of change of occupants of the property.

According to a second aspect, a financial instrument defining an interest in a property is provided, the interest providing one or more interest buyers with rights on at least part of a selling price of the property, the interest being purchasable by the interest buyers independently of time of sale of the property and independently of change of occupants of the property.

According to a third aspect, a financial instrument is provided, wherein habitational rights in a habitable property and non-habitational rights of the habitable property are defined and wherein the habitational rights are separated from the non-habitational rights.

According to a fourth aspect, a market index to predict value of a home is provided.

According to a fifth aspect, a twin options instrument is provided, wherein a first party obtains the right to exercise an option for a first entity, while a second party obtains the right to exercise an option for a second entity.

According to a sixth aspect, a method whereby a seller can determine a set of bidders which allow him to raise more than a certain amount of money for the least amount of equity is provided, comprising: i) examining each bid, starting with the highest bid; ii) accepting that highest bid, awarding that highest bid an amount of equity equal to the minimum between the amount of equity the seller wishes to award and the amount of equity the bidder wishes to buy; and iii) if the seller wants to raise more money, removing that bidder is from the pool of bidders under consideration, and repeating i) and ii).

Further embodiments will be provided throughout the specification and claims of the present application.

In accordance with the above aspects, real estate selling decisions can be put strictly in the hands of professionals, where they belong.

The present disclosure can be seen as uncoupling two events to eliminate the requirement of the co-occurrence of any combination of multiple events (e.g. simultaneity or co-location), reducing an event with rate or probability p(x) p(y) to one with min(p(x),p(y)), which greatly increases its rate or probability. This kind of uncoupling has already been seen in other fields. The car eliminated the need for two places to be within walking/riding distance in order to make them accessible. The telephone, the telegraph and the fax eliminated the requirement of two people needing to be at the same place in order to communicate. Email, World Wide Web (WWW) and voicemail have been so successful because they carried out a double uncoupling: they eliminated the requirement for sender and receiver to be in the same place or communicate at the same time: writing and reading (speaking and hearing) can happen at different times, eliminating the need for lengthy phone tags, allowing users to communicate in their pajamas at their convenience, even if that means ungodly hours.

In particular, the present disclosure simultaneously carries out the following uncouplings:

(1) releases seller and buyer of any given property from the need to transact at the same time and/or place, (2) releases someone moving from one property to another from the common need to sell old property and buy new property at the same time, (3) uncouples the entity to decide on the best price, time to sell and selling mechanism from the previous owner of the property, (4) the need for all the money to compensate the seller of a property for the sale to come from the buyer or even one person or entity, and (5) the owner of all residence rights in a property from the owner(s) of financial interest in the property.

A further type of historic uncoupling, which has its counterpart in another part of the present disclosure, relates to breaking the need for a sale of a large-ticket item to have a single owner. If today's large public corporations had to have a single owner, they would never have raised the capital they needed to grow. Imagine having to find a single individual to buy Time Warner. Yet houses today are sold only to single entities, not shareholders.

Also disclosed is a new type of financial instrument which reduces the risk of home ownership, at the same time as it makes the benefits of home ownership more affordable. It differs from rentals in many respects, not the least of which is that the occupant of a rental property can be evicted at any time by the landlord(s) and has no financial incentive for home improvement.

DETAILED DESCRIPTION First Financial Instrument

According to a first embodiment, the present disclosure provides a new financial instrument, which allows one or more buyers to purchase an interest in a property (e.g., a home, a building or deed of land) from a seller independently of the time of the sale of the property and independently of change of occupants of the property. According to one aspect, options can be sold and bought for habitational as well as non-habitational components of the property.

More specifically, the buyer can buy the interest at any time before the time of sale of the property. The buyer(s) of the interest may or may not be able to make some decisions on the sale of the property. Moreover, the buyer of the interest will get part or all of the selling price of the property. A first kind of interest could involve, for example, an option to the living rights to a house. As soon as the option tied to this interest is exercised, the buyer of the interest will own the living rights to the house. If living rights and non-living rights are separated, then this buyer will also be entitled to the selling price of the property, if he decides to sell it. A second kind of interest could involve, for example, rights to a fraction of the sale price of the house. The rights given to the buyer of the interest can include decision rights, such as decisions on the auction mechanism of the sale, decisions on the price of the sale, and so on.

The seller may reserve some of these rights for himself, though. For example, the seller may not provide the buyer of the interest with the right to decide the time of sale of the property.

Alternatively, the rights provided to the buyer may specify that the sale should not happen before the seller of the interest has found an alternate home. In any case, according to this financial instrument, the sale of the above rights over a sale price is dissociated from the time of the sale and change of the occupants.

The interest above can have an expiration date. Further, by way of example and not of limitation, the financial instrument disclosed herein can also be combined with a second financial instrument which deals with habitational and non-habitational rights of a habitable property. The second instrument will be explained later.

On the seller side, what the seller wants is the certainty that he will have the money he wants to buy a new house when he/she finds such new house. On the buyer's side, what the buyer wants is to make a profit for his willingness to provide such security. Therefore, this financial instrument can be seen as the seller buying or selling an option to the house based on the money he wants for the house (e.g., $500,000) and then starting to look for a house to move into. For example, the seller might buy a put option that gives him the right to sell the house for a certain amount within a certain period of time. In some embodiments, both the seller of the interest (i.e. the proprietor of the house) and the buyer of the interest put something in escrow. The seller puts the title to the house while, the buyer puts the money. Scenarios where the seller of the interest puts less than the title to the house in escrow include embodiments where the buyers could be multiple buyers, so that neither gets the title, but just a right to a fraction of the selling price.

The buyer of the interest could be just a regular buyer who wants to live in that house or somebody who wants to resell the interest. In the latter case, the buyer can, at some point, begin a process (e.g., an auction) to find a second buyer who wants to live in the house.

Meanwhile, when the seller of the interest finds another house, he exercises the option, gets the amount of money tied to the option ($500,000 in the above example) and relinquishes rights to the house. On the buyer's side, the buyer has two options: the buyer keeps the relinquished title (either because he wants to live in that house himself or because he has not found a second buyer yet at the time of exercising the option or 2) the title goes to a second buyer, found by the first buyer in the auction process above. So, if the buyer sells the title to the house to a second buyer for $700,000, he makes a profit of $200,000.

In accordance with this first financial instrument, seller and buyer of a house are released from the need to transact at the same time and place by allowing a third party (the buyer of the interest) to buy rights to the sale price of a house. Since these investors may not be looking to live in the property, they are willing to buy that instrument before the seller is ready to vacate the house/apartment/property. The seller of the interest now can count with the money he or she needs to buy a new house, and go and buy a new house without time pressure, because he or she does not need to worry about buying and selling his/her current house around the same time.

In another related embodiment disclosed here, a pair of options may be exchanged, such that one party X obtains the right to exercise an option for A (e.g., obtain an amount of money M from party Y in exchange for certain rights to a property) while a second party Y obtains the right to exercise an option for B (e.g., obtain certain rights to a property in exchange for an amount of money N). The timing rights of such “twin” options need not be identical. For example, X may obtain a right to exercise his option anytime in the next 120 days, whilst Y's option may not allow him to exercise his option until the end of the 120 days. Such a pair of twin options allows the seller of a property time to find a place to move out while providing the buyer of the property with a concrete right to the property that he/she may sell. Note that the price of both options in the twin pair need not be identical: either one could be bigger, resulting in either party paying the other for such rights exchange.

By way of example, let's imagine that Alex sells an option to the living rights to his townhouse for $650,000 to John. Knowing that he will count with $650,000, Alex now goes into the market to buy a bigger house. Two months later, he finds the house he wants at $ 900,000 and buys it. He exercises the option, gets $650,000 from John, and John now owns the living rights to the townhouse that Alex used to live in. It should also be noted that John can sell his option at any time to anybody in the market, so he can get liquidity before the house actually changes occupant. In this example, owning the living rights means to have complete title to the house.

Obligations of a party related to an option can also change hands in a transaction. In other words, if Alex sells an option to sell his house for $650,000, Alex can pay a third party to release him from this obligation and assume it himself.

This financial instrument according creates an options market for housing, creating liquidity, so that a person (John, in the above example) can buy a right to receive the sale price of a house before habitation ownership of the house changes hands. The financial instrument also creates an equity structure for housing, so that fractional ownership is possible. Some issues should be addressed:

a) In some embodiments, the buyer of the house will want to ensure that the inhabitant (i.e. seller of the interest) should leave the house at some point. In one embodiment, this is done using the twin option structure above to give the buyer of the house the right to the house by a certain date. b) It should be determined who decides to whom to sell the house and for how much. In one embodiment, this is done by an instrument defining sale decision rights, which gets valued by the marketplace.

According to a further embodiment, the seller can sell rights to a fraction of the sale price of the house. In such embodiment, Alex would sell to John, say, rights to 60% of the sale price for, say, $360,000. When later the house is sold for, say, $1,000,000, John gets $600,000. An escrow in not necessary. For example, Alex could have a contract with John, according to which John gets 60% of the sale price.

According to a further embodiment, fractional ownership of the interest is also provided. This means that the need for all the money to compensate the seller of a property for the sale of the interest to come from the buyer or even one person or entity is eliminated. In this respect, the person skilled in the art will understand that when multiple owners/fractional property exists for a property, some type of management, or the right to make the decision to sell, should be defined. According to a further embodiment of the present disclosure, this right itself has its own value in the marketplace. Therefore, the buyer of such right may pay a premium of $50,000 for the decision rights, namely the right to decide whether to accept an offer to buy or not. The decision rights holder will have a fiduciary duty to act in the interest of the stockholders. In other words, the decision rights holder cannot sell the house to a friend for less than another buyer has expressed willingness to pay. According to another embodiment, the decision rights belong to any majority of stock in the property, so that stockholders vote on each sale and a majority is needed to approve it.

According to yet another embodiment of the present disclosure, an index is provided to predict the value of a home, given its price relative to an index of similar houses in the past, and the evolution of the index since. This allows buyers to bid on a property sight unseen. For example, let's say that in 1990, the median Pasadena home is worth $250,000 and Alex's house is worth $500,000. When Alex puts his house in the market in 2008, the median Pasadena home is worth $500,000, and so the index predicts Alex's house to be worth $1,000,000. The person skilled in the art will understand that indexes can group homes by other criterion than city alone, and can be rather complex, e.g., a coefficient times the median home value in the city+another coefficient times the median home value in the block+another coefficient times the median home value for houses which were in a given price range within a given date range.

Second Financial Instrument

The present disclosure also provides a second type of financial instrument. This second financial instrument dissociates living or habitational rights from equity ownership in a real estate property. This instrument allows a home buyer to raise capital from investors interested in investing in the piece of real estate he wants to inhabit. In an auction market, for example, the bidder who bids the most for habitational rights gets them. Likewise, equity without living rights in the household (i.e. non-habitational rights) is also auctioned off to the highest bidders using one of multiple auction methods known to one versed in the art. For example, these non-living or non-habitational rights can be auctioned off to the highest bidder at the bid given by the second highest bidder, or at the price offered by the highest bidder. Habitational rights can be defined as usage rights involving no habitation, e.g. the right to use an office space or the right to plow a piece of land.

The person skilled in the art will understand that while there is a single habitational right per household (i.e. all owners of living rights to a household must consent to every other such holder), there may be multiple independent shareholders with non-habitational rights. However, although there will be a single habitation right per habitable property, such single habitational right can be owned by a plurality of holders, and all those holders will have to consent to the sale to a new buyer, in order for the new buyer to acquire the single habitation right. The one or more non-habitational rights can be sold to other buyers of non-habitational rights or cashed out when the habitable property is sold.

Habitational rights can also involve ownership of a fraction of the value of the property, right which can be sold like any security, or cashed out when the property is sold. This feature is similar to the owners of stock in a corporation being entitled to a portion of the sale value of the company. For example, habitational rights can confer equity rights according to a formula.

In particular, according to a first aspect, such portion can be a fraction X=H/T, where H is the last sale value of habitation rights and T is the sum of H and the aggregate value of non-habitation rights in the property at the time of the last sale.

Alternatively, according to a second aspect, such portion can be a fraction X=H/T, where H is the last sale value of habitation rights and T is the sum of H and the current aggregate value of non-habitation rights in the property, with T fluctuating with the market.

According to a third aspect, another way of determining the portion is to let the market at the time of each house sale determine the fraction X. For example, each party who wants to buy non-habitational shares can specify the price they are willing to pay per percentage point of the next sale price and the number of percentage points they want to buy. For example, one might expect the house to sell for more than $1 million and bid $9,000 per percentage point and ask to buy 0.5 percentage points. If this bid is accepted by a seller who holds stock in the house, the party buying the non-habitational shares pays the seller $4,500 and that party is now entitled to 0.5% of the appreciation given by the difference between the house's next selling price and the previous one. There is a fixed number of shares of any house (e.g., 1,000, each worth 0.1% of the value of the house) plus the habitational right. According to this embodiment, the habitational right does not entitle its owner or holder to get any fraction of the appreciation of the house, it just entitles such holder to live in the house and to get, upon the sale of the house, the money that they paid for the habitational rights.

By way of example, let's consider the extreme case in which the holder of the habitational right holds no interest in the change in sale price from when he/she bought it to when he/she sells it. In this case, the entire appreciation, given by the new sale price minus the old sale price, goes to the holders of non-habitational rights. So, if Alex bought the habitational rights for $500,000 and sells them for $700,000 later, the $200,000 go to the holders of the non-habitational rights (“appreciation stock”). The $500,000 will go to Alex. If, on the other hand, the house is sold for less than Alex paid for it (e.g., $400,000), then the options of the non-habitational rights holders are “under water” and no monies are distributed to them: the $ 400,000 go to Alex as the holder of the habitational right.

The opposite extreme is the current system: as a holder of the habitational right, Alex would own also 100% of the non-habitational rights or “appreciation stock”, and so the entire sale price goes to Alex.

In the middle lie all other ratios. A preferred embodiment of determining the ratio has the market determine it. For example, when a buyer buys a house, he or she decides what fraction he wants to sell options (or “non-habitational rights”, or “appreciation stock”, which terms are used interchangeably) for. The market then determines how much to pay for them. For example, Alex might buy a house for $500,000 and decide to sell 500 of the 1,000 0.1% shares of appreciation stock. If the market pays a price of $200/share, that means that Alex gets $100,000 to help bear the expenses of Alex's purchase, but Alex is giving up 50% of the appreciation when Alex sells the house. According to a further aspect of this embodiment, Alex could always sell more shares later or rebuy some.

Other embodiments of this second financial instrument can further provide that also the sale price, and not just the appreciation, is divided between holders of non-habitational rights and habitational rights.

In some embodiments, when a house or property sale occurs, the owners of non-habitational rights get paid (if the new sale price exceeds the value at which they get paid, e.g. the previous sale value), after which their rights expire. The new home buyer can now sell non-habitational rights to offset the price he pays. This can happen in a different order: bidders for non-habitational rights may place bids prior to the home purchase, which the buyer of the house can use to afford the house.

One way in which these bids can be placed is by placing a bid for a fraction of the non-habitational rights or equity of the property. Let's say Peter wants to buy a house. The seller is asking for $1,000,000. Peter can only afford to pay $500,000. He browses the top bidders for that property (note that the bidders may be bidding for any property (or set of properties) that meets certain requirements (e.g. in an area and/or a price range); once their bid has been accepted by a given home owner, the bid goes off the market for all other properties), and finds that there is a set of bidders willing to pay $500,000 for 60% of the house equity. Peter accepts those bids and pays $500,000 to buy the habitational rights plus 40% of the house equity. The house equity can continue to be traded continuously and change hands and price per market fluctuations. When Peter sells the house, if he is still holding on to 40% of the house equity rights, he gets 40% of the sale price, with the remaining 60% going to the remaining equity right holders. The new buyer(s) now own the equity rights.

A related aspect disclosed here involves a method and system whereby a person can determine the set of bidders which allow him to raise more than a certain amount of money for the least amount of equity. For example, in the example above, Peter wants the set of bids that amounts to $500,000 or more that demands the least amount of equity in his property. The system determines this by examining each bid, starting with the highest bid, and accepting that highest bid, awarding it an amount of equity equal to the minimum between the amount of equity the seller wishes to award and the amount of equity the bidder wishes to buy. If the seller wants to raise more money, that bidder is removed from the pool of bidders under consideration, and the process is repeated.

One of the issue that remains to be solved would be the lack of incentive for the owner of habitational rights to maximize the value of sale. A first solution to this problem is that the owner of the habitational rights gets a part of the price increase or must own some equity rights. A second solution is that the sale price has to be approved by a majority of (or some subset of) equity right holders.

This dissociates the speculative aspect of property buying from the habitational one, allowing investors to profit from appreciation while making home ownership more affordable.

Other embodiments of this second financial instrument can further provide that also the sale price, and not just the appreciation, is divided between holders of non-habitational rights and habitational rights.

In summary, this second instrument takes advantage of the fact that investors would be willing to “foot the bill” for part of the purchase price of a home if they can benefit from it as an investment, and has several desirable properties:

(1) it enables home buyers of modest resources to own habitation rights in a home and to partake in the financial benefits of home improvement even if they cannot afford the whole value of the home. Unlike mortgages, equity financing does not commit a homeowner to debt, and is available to people who cannot afford interest payments. (2) it makes the housing market more liquid, allowing for more rapid and efficient transactions, lower downtime, etc. (3) it provides the market with instruments to invest in real-estate without reducing the pool of housing available for live-in home-owners. (4) it allows homeowners to buy a relatively small equity stake in a large house, allowing capital to effectively raise the standard of living.

Combination of First and Second Financial Instrument

Habitational rights and non-habitational rights are particular kinds of interests that allow their buyers to make some decisions on the sale of the property. Therefore, combinations of the first and second financial instruments are also possible.

In this respect, it should be determined where the money paid by the buyer of the habitational rights goes. In one embodiment, it goes to the owner(s) of the habitational rights. This has the disadvantage of making the non-habitational rights rather “bubblish” in that they are not tied to any non-stock transaction. In another, preferred, embodiment, part of the price of the habitational rights goes to the non-habitational rights holders, the amount being determined by the market. So, for example, if a house is sold for $1,000,000, and the habitational rights go for 60% or $600,000, $400,000 would be distributed to the owners of the non-habitational rights.

Stock Market

According to an embodiment of the present disclosure, a real-estate stock market is provided, that allows an owner to easily find a buyer for his/her house or multiple buyers for non-habitational equity interests in his/her house at any time, e.g. via the World Wide Web (WWW). Presence of such market is useful, for example, when determining prices for the second financial instrument. Additionally, such market allows buyers and sellers to sell the non-habitational and habitational rights in the manner of the Dow® or Nasdaq® stock market. Presence of such a market provides liquidity and opportunity for fractional ownership.

Accordingly, what has been shown are financial instruments and methods for the housing market. While these instruments and methods have been described by means of specific embodiments and applications thereof, it is understood that numerous modifications and variations could be made thereto by those skilled in the art without departing from the spirit and scope of the disclosure. It is therefore to be understood that within the scope of the claims, the disclosure may be practiced otherwise than as specifically described herein. 

1. A financial method comprising: providing one or more interest buyers with an interest in a property, the interest providing the one or more interest buyers with rights on at least part of a selling price of the property, the interest being purchasable by the interest buyers independently of time of sale of the property and independently of change of occupants of the property.
 2. The financial method of claim 1, wherein the rights of the interest are selected from the group consisting of auction mechanism for the sale, price of the sale, and time of the sale.
 3. The financial method of claim 1, wherein the interest has an expiration date.
 4. The financial method of claim 1, wherein the interest is a habitation right of a habitable property.
 5. The financial method of claim 1, wherein decision to sell the instrument to the buyer and cost of purchasing the instrument are defined by sale decision rights.
 6. The financial method of claim 1, wherein decision to sell the instrument to the buyer and cost of purchasing the instrument are defined by a housing stock market.
 7. The financial method of claim 1, wherein some rights to the selling price of the property are reserved for a seller of the interest.
 8. The financial method of claim 1, wherein the rights on at least part of a selling price of the property include non-habitational rights.
 9. The financial method of claim 1, wherein the interest is resellable by the interest buyer to a further buyer.
 10. The financial method of claim 1, wherein there is a plurality of interest buyers defining fractional ownership of the interest.
 11. The financial method of claim 1, wherein the interest also comprises sale decision rights.
 12. A financial instrument defining an interest in a property, the interest providing one or more interest buyers with rights on at least part of a selling price of the property, the interest being purchasable by the interest buyers independently of time of sale of the property and independently of change of occupants of the property.
 13. A financial instrument wherein habitational rights in a habitable property and non-habitational rights of the habitable property are defined and wherein the habitational rights are separated from the non-habitational rights.
 14. The financial instrument of claim 13, wherein a single habitational right per habitable property is defined, and one or more non-habitation rights are defined.
 15. The financial instrument of claim 14, wherein the single habitation right and the one or more non-habitation rights are sold by way of auction.
 16. The financial instrument of claim 14, wherein, were the single habitation right is owned by a plurality of holders, all holders of the plurality of holders have to consent to the sale to a new buyer, in order for the new buyer to acquire the single habitation right.
 17. The financial instrument of claim 14, wherein the one or more non-habitation rights can be sold to other buyers or cashed out when the habitable property is sold.
 18. The financial instrument of claim 14, wherein the holder of the single habitation right is entitled to a portion of the sale value of the habitable property.
 19. The financial instrument of claim 18, wherein the portion is a fraction X=H/T, where H is the last sale value of habitation rights and T is the sum of H and the aggregate value of non-habitation rights in the property at the time of the last sale.
 20. The financial instrument of claim 18, wherein the portion is a fraction X=H/T, where H is the last sale value of habitation rights and T is the sum of H and the current aggregate value of non-habitation rights in the property, with T fluctuating with the market.
 21. The financial instrument of claim 18, wherein the portion is defined by a housing stock market.
 22. A market index to predict value of a home.
 23. A twin options instrument, wherein a first party obtains the right to exercise an option for a first entity, while a second party obtains the right to exercise an option for a second entity.
 24. The twin options instrument of claim 23, wherein the timing of the two options is not necessarily identical.
 25. The twin options instrument of claim 23, wherein the price of the two options is not necessarily identical.
 26. A method whereby a seller can determine a set of bidders which allow him to raise more than a certain amount of money for the least amount of equity, comprising: i) examining each bid, starting with the highest bid; ii) accepting that highest bid, awarding that highest bid an amount of equity equal to the minimum between the amount of equity the seller wishes to award and the amount of equity the bidder wishes to buy; and iii) if the seller wants to raise more money, removing that bidder is from the pool of bidders under consideration, and repeating i) and ii). 